The influence of autofrettage with bauschinger effect on the SIFs of multiple longitudinal coplanar cracks in pressurized cylinders

The influence of the Bauschinger Effect (BE) on the three dimensional. Mode I, Stress Intensity Factor (SIF) distributions for arrays of longitudinal coplanar, surface cracks emanating from the bore of a fully or partially autofrettaged thick-walled cylinder is investigated. The generation and comparison of the SIFs for a "realistic" - Bauschinger Effect Dependent Autofrettage (BEDA) and those for an "ideal" - Bauschinger Effect Independent Autofrettage (BEIA), which until now did not exist, is undertaken. The 3-D analysis is performed via the finite element (FE) method and the submodeling technique, employing singular elements along the crack front. Both autofrettage residual stress fields, BEDA and WEIA, are simulated using an equivalent temperature field. More than 250 different crack configurations are analyzed. SIFs for various crack densities (2c/d=0.25-0.75), a wide range of crack depth to wall thickness ratios (a/t=0.01-0.25), various ellipticities (a/c=0.5-1.5), and different levels of autofrettage (ε=30%-100%) are evaluated. The Bauschinger Effect (BE) is found to significantly lower the beneficial stress intensity factor due to autofrettage, K_IA by up to 52%, as compared to the case of "ideal" autofrettage. The reduction in K_IA varies along the crack front with the maximum determined by the crack ellipticity, crack depth and crack separation distance. In some cases the maximum occurs at the deepest point of the crack and in others the maximum is at the point of intersection between the crack plane and the inner surface of the cylinder. In certain situations, the maximum transitions from one to the other as crack density increases. The detrimental influence of the BE increases as the crack density decreases and as crack depth decreases. For a partially autofrettaged cylinder, as the level of overstrain becomes smaller the influence of the WE is considerably reduced. As a result, the SIFs due to 100% BEDA differ by less than 15-17% when compared to 60% BEDA, and on the average the difference is only about 6%. Furthermore, the results indicate that crack density, and, in some cases, crack depth and crack ellipticity have opposing effects on the SIF of longitudinally coplanar crack arrays.